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Product representation of default bilattices

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If you have a question about this talk, please contact Paul Levy.

Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices can be used to model situations in which information is prioritised and so can be viewed hierarchically in terms of levels of default. The best-known bilattice allowing for defaults was introduced in 1986 by M.L. Ginsberg under the name SEVEN ; this models a single level of default. Subsequently bilattices encompassing additional levels of default (TEN, ...) have been exploited in the AI literature.

But SEVEN is not interlaced, and nor are other default bilattices: the lattice operations of one lattice structure do not preserve the order of the other one. Consequently default billatices fall outside the scope of the principal tool of bilattice theory, namely the Product Representation Theorem (which underpins, in particular, the work of Achim Jung and Umberto Rivieccio on bilattices).

In this talk I shall introduce joint work with Leonardo Cabrer and Andrew Craig which develops a topological duality theory in the context of prioritised defaults. This leads on to a generalisation of the traditional product representation for interlaced bilattices, and shows how twist structures arise in a natural way in the representation of SEVEN , TEN, and beyond.

This talk is part of the Theoretical computer science seminar series.

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